Rewrite as a simplified fraction. ${0.6\overline{8} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 68.8888...\\ 10x &= 6.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 62}$ ${x = \dfrac{62}{90}} $ ${x = \dfrac{31}{45}} $